SOLUTION: The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?

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Question 746903: The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?
Answer by timvanswearingen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the length of the base.
Then the height can be represented as h=2x%2B5 (5 units more than twice the base)
Now, the formula for the area of a triangle is A=b%2Ah
So, 21=%281%2F2%29%2Ax%2A%282x%2B5%29
Using the distributive property,
21=x%5E2%2B%285%2F2%29x
Subtract 21 from both sides,
0=x%5E2%2B%285%2F2%29x-21
Now, using a=1, b=5/2, and c=-21, plug into the quadratic formula.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



x+=+%282.5+%2B-+sqrt%28+6.25%2B168+%29%29%2F4+

x+=+%282.5+%2B-+sqrt%28+174.25+%29%29%2F4+

There are two possible answers. x=%282.5%2B+sqrt%28+174.25+%29%29%2F4 or x=%282.5-+sqrt%28+174.25+%29%29%2F4
The second answer would result in a negative number. Since we are trying to find out the length of the base of a triangle, we can throw out the negative answer.
Thus, x=%282.5%2B+sqrt%28+174.25+%29%29%2F4
So x is about 3.925 units.
x was representing the base. Since the height was 2x+5, simply plug in the x value found above to find the height.
h=2x%2B5
h=2%2A%283.925%29%2B5
h=7.850%2B5
h=12.850 units